File:One arm spiral - part of Mandelbrot set.png

#!/bin/bash
# test rays crossing image borders in both directions
# chmod +x *.sh

# angle or external parameter ray 
angle=63/33554432
# info from program Mandel by Wolf Jung http://mndynamics.com/indexp.html
# The angle  63/33554432  or  0000000000000000000111111
# has  preperiod = 25  and  period = 1.
# Entropy: e^h = 2^B = λ = 1.14436377
# The corresponding parameter ray is landing at a Misiurewicz point of preperiod 25 and period dividing 1.

# one can use this script for making sequence images ( n.png) and text files ( n.txt) from 0 (zoom= 0 means  no zomm ) to zoom=40 ( tested)

# zoom exponent : if zoom = 0 then no zoom, if 1 then radius is 10 times smaller
zoom=40
# zoom=30 ./render using MPFR<114> time = real	10m2.216s
# zoom=40 ./render using MPFR<149> time = real	57m21.769s

# depth of drawing external ray 
depth=1500 
# inbits are proportional to zoom 
inbits=$((54+$((4*$zoom))))

# view = plane description  = center and radius 
# center can be aproximated by last point of the ray 
# ./ray_in 63/33554432 1500 > ray.txt
center="2.75440192442997482763156942365466633744567027411676641366606788332e-1 6.43937272885086260909220730125585919267993168198975635957506121777e-3"
# radius = (image height/2)
radius="1.5e-"$zoom
view=$center" "$radius

length=$((${#center}/2))
# echo " length of string =" $length

# image size in pixels 
iWidth=2560
iHeight=1440
maximum_iterations=4096
escape_radius=512
#          1    2  3      4             5    6     7       8                  9    
# ./render cre cim radius escape_radius stem width height maximum_iterations  interior
arguments=$view" "$escape_radius" out "$iWidth" "$iHeight

echo "making png image "
pngfilename=$zoom".png"
# render image
# heredoc syntax 
./render $arguments && ./colour > out.ppm && ./annotate out.ppm  $pngfilename <<EOF
rgba 1 1 1 1
line ./ray_in $angle $depth | ./rescale $inbits 53 $view 0
EOF

echo "Image " $pngfilename "is saved"